2 Answers
2

The d20 class rules are flexible enough that there isn't much need for specific classes by faction; class determines professional skills. (It's a design principle of d20 that anything focused enough to be faction-specific should be a prestige class. Officers of any military could have Noble levels, for example... when you get right down to it, being a scout or fighter pilot is the same whoever you fight for.) There are some good examples of this scattered across various rulebooks.

That said, the Hero's Guide is the faction-specific-characters book, and has several prestige classes particularly aimed at Imperial characters:
Black Sun Enforcer, Black Sun Vigo, ISB Special Agent and Sienar Engineer.

A few other prestige classes are good matches:
The base military classes: Elite Trooper, Officer, Starship Ace (Main Rulebook)
Bodyguard (in the Ultimate Alien Anthology) or Loyal Protector (Hero's Guide) are good for Imperial / senatorial guards.
Chief Engineer (Hero's Guide) is another likely example.

The Hero's Guide also offers some good example builds for an Imperial Officer using the standard Soldier/Noble/Officer classes. It's probably the best answer to your question, as it also has some relevant feats (Aristocrat's Honor, Combat Veteran, Diplomatic Immunity, Gun Crew Chief, Political Pull, Flight Academy Training, Imperial Command Training) and the faction rules/ideas.

Also, two Pre-RE prestige classes are specifically Imperial: The Emperor's Hand and Imperial Inquisitor (both in the Dark Side sourcebook). Both should work with minimal conversion in RE.
(Also, the Rebellion Era sourcebook obviously has a lot of general information and character templates. No classes though, unless I remember wrongly.)